{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "cc754f35",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import time\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "912a2532",
   "metadata": {},
   "outputs": [],
   "source": [
    "L=100\n",
    "R=1000000\n",
    "# шаг измерения R, Будет прибавлять на \"шаг\" к текущему R в цилке\n",
    "step = 100000\n",
    "\n",
    "c=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "2e729d60",
   "metadata": {},
   "outputs": [],
   "source": [
    "#функция замера времени подсчета НОД\n",
    "def nod_time(lst):\n",
    "    #фиксируем время начала\n",
    "    start_time = int(round(time.time() * 1000))\n",
    "    math.gcd(*lst)\n",
    "    #Фиксируем время конца операции\n",
    "    end_time = int(round(time.time() * 1000))\n",
    "\n",
    "    howmtime = end_time - start_time\n",
    "    print(\"Затрачено милисекунд на поиск НОД: \", howmtime)\n",
    "    \n",
    "    return howmtime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "2fb418c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R</th>\n",
       "      <th>gdc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [R, gdc]\n",
       "Index: []"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = pd.DataFrame(columns=[\"R\", \"gdc\"])\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "4029a181",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Затрачено милисекунд на поиск НОД:  108\n",
      "189\n",
      "Затрачено милисекунд на поиск НОД:  108\n",
      "190\n",
      "Затрачено милисекунд на поиск НОД:  107\n",
      "191\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Затрачено милисекунд на поиск НОД:  108\n",
      "192\n",
      "Затрачено милисекунд на поиск НОД:  160\n",
      "193\n",
      "Затрачено милисекунд на поиск НОД:  105\n",
      "194\n",
      "Затрачено милисекунд на поиск НОД:  106\n",
      "195\n",
      "Затрачено милисекунд на поиск НОД:  114\n",
      "196\n",
      "Затрачено милисекунд на поиск НОД:  105\n",
      "197\n",
      "Затрачено милисекунд на поиск НОД:  105\n",
      "198\n",
      "Затрачено милисекунд на поиск НОД:  111\n",
      "199\n"
     ]
    }
   ],
   "source": [
    "i=0\n",
    "#посчитаем некоторое количество значений\n",
    "for i in range(1,200):\n",
    "    #записываем значения от L до R в список\n",
    "    c = list(range(L, R))\n",
    "    #вычисляем скорость вычисления по ранее написанной функции\n",
    "    gdc_t = nod_time(c)\n",
    "    \n",
    "    #записываем значения R и времени на подсчет НОД в Pandas\n",
    "    new_row = {'R':R,'gdc':gdc_t}\n",
    "    results = results.append(new_row, ignore_index=True)\n",
    "    \n",
    "    #добавляем шаг к R\n",
    "    R = R + step\n",
    "    #смотрим на какой итерации i мы сейчас находимся\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "e23ac5c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R</th>\n",
       "      <th>gdc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10000000</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10010000</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10020000</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10030000</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10040000</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>11940000</td>\n",
       "      <td>106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>11950000</td>\n",
       "      <td>114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>11960000</td>\n",
       "      <td>105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>11970000</td>\n",
       "      <td>105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>11980000</td>\n",
       "      <td>111</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>199 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            R  gdc\n",
       "0    10000000   93\n",
       "1    10010000   89\n",
       "2    10020000   92\n",
       "3    10030000   90\n",
       "4    10040000   96\n",
       "..        ...  ...\n",
       "194  11940000  106\n",
       "195  11950000  114\n",
       "196  11960000  105\n",
       "197  11970000  105\n",
       "198  11980000  111\n",
       "\n",
       "[199 rows x 2 columns]"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#проверяем данные в таблице\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "d94c54db",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 7200x5040 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#нарисуем график, x - значения R, y - значения времени вычисления\n",
    "plt.figure(figsize=(100, 70))\n",
    "plt.plot(results['gdc'],results['R'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6a27b52",
   "metadata": {},
   "source": [
    "Если сравнить графики с https://www.bigocheatsheet.com/ можно сделать вывод, что вычисление O нотации в math.gcd ближе всего к O(n^2), но сильно зависит от количества элементов в списке, по которым мы вычисляем НОД."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
